Photon number resolution with SNSPD arrays

Photon number resolving (PNR) single photon detection is an ultimate resource for quantum optics, enabling a range of applications in photonic quantum sensing, communications, and computing. In such applications, superconducting nanowire single photon detectors (SNSPDs) are preferred for high efficiency, high rate, low jitter, and low noise detection of single photons. Recent advancements in SNSPDs have led to large-scale arrays of nanowires integrated on a single chip, enabling demonstrations of spatially-multiplexed pseudo-PNR detection up to 100 photons, as well as photon number resolution with individual nanowires. Combining both of these developments could lead to unprecedented levels of photon number resolving capabilities. Here we theoretically and experimentally investigate the PNR capabilities of arrayed detectors. We present, for the first time, a generalized recursive equation and its closed form solution for the positive operator valued measure (POVM) of detectors arrays with arbitrary splitting coefficients, important for practical realizations of large arrays with non-uniform spatial distributions of incident photons. We reconcile our POVM model with experiments that reconstruct the POVM of state-of-the-art SNSPD array detectors, namely 1) the 32-pixel Performance-Enhanced Array for Counting Optical Quanta (PEACOQ) detector and 2) an array of PNR SNSPDs each capable of resolving up to 5 photons. Our work supports development of large-scale arrays of PNR SNSPDs, towards the prospect of ultra-high photon number resolution with arrayed single photon detectors.